The risk of not being normal in finance. An essay on the leptokurtic behavior of stock series in Colombia

This paper is aimed at analyzing the main problems concerning fat-tailed asset return distributions. In doing so, a sample of Colombian stock returns over a period of time ranging from 2001 to 2010 is considered. The main conclusion drawn from this case study is that any model facing leptokurtosis has to take into account the particular informational issues related to stationary-normality tests of stock-market return series; the best fitting criteria which include the main no normal characteristics of empirical return distributions by stock groups; the idiosyncratic aspects of those stocks showing differentiated behaviors; and the final statistical evaluation by the risk-manager. Ignoring any of these steps means overlooking the well-documented financial fact that empirical fat-tailed return distributions are not the same in all markets, and that neither are they caused by the same reasons. Leptokurtosis is a particular problem of any stock market, and so there is no universal statistical method to deal with it.